Applications of quadratic functions

Question

A golf ball is projected upward from ground level at an initial velocity of 112ft/sec. The height of a projectile can be modeled by s(t)= -16t^2 + vt + s, where t is time in seconds, S is the initial height in feet, and v is the initial velocity in ft/sec.

A. How high will the ball be after 2 sec?

B. What is the maximum height the ball reaches?

C. When will the ball reach the ground?

Answer 1

s(t)= -16t² + vt + s

Plugging in the values provided, initial velocity = 112, it is hit from the ground, therefore s=0

s(t)= -16t² + 112t

A. To find the height at 2 seconds, plug in 2 for t

s(2)= -16(2)² + 112(2) = 160 ft

B. To find the maximum height, I used the graphing calculator max feature to find the vertex is (3.5, 196)

The max height is 196 ft

C. To find when it hit the ground, I also use the graphing calculator to find the zero at t = 7 seconds